Soldiers are self-sufficient builds IF they have enough ammo. You therefore have to be good at shooting, and watch out for enemies that can regenerate their protections or health. There are ways to stop health regeneration, but if enemies are able to raise their protections again, that can be a huge drain on ammo. Also, there are missions where you face endless waves of enemies until you reach certain invisible checkpoints or accomplish certain goals.
The only attack power that doesn't involve ammo is Concussive Shot, but that inflicts weak damage and the knockdown will only work on enemies without protection.

Adrenaline Rush
Double damage. You want to maximize the duration of this so you do not have to constantly invoke it.
The difference between Hardened Adrenaline Rush and Heightened Adrenaline Rush on rank 4 is a hard choice. If you play very aggressively and are willing to fight when injured, go for Hardened and the damage reduction. If you play conservatively to avoid damage AND prefer to place single high-damage shots, then go for Heightened Adrenaline Rush.
The damage-per-second is actually higher with Hardened Adrenaline Rush:

Hardened: DPS x 0.5 time x 200% damage = 100% DPS

Heightened: DPS x 0.3 time x 240% damage = 72% DPS

However, DPS is only relevant when you are using weapons with a high rate of fire, and it is relative to the time passing for YOU, not the enemy. With Hardened Adrenaline Rush, 10 seconds of time for you is 5 seconds of time for the enemy. With Heightened Adrenaline Rush, 10 seconds of time for you is only 3 seconds for the enemy. Damage per shot is 200% with Hardened and 240% with Heightened. To maximize the value of your ammunition, go for Heightened Adrenaline Rush.

Concussive Shot
This fires a round at the target, but uses no ammunition. We use Shepard's last talent point here instead of Cryo Ammo because of this, but it really doesn't matter unless you do not choose an Advanced Power that does damage, in which case definitely go for Concussive Shot since it then becomes your only damage alternative if you run out of ammunition (i.e., thermal clips).
Concussive Shot is very strong against Barriers, but of course does not knockdown until all protections are down.

Ammo Powers: Disruptor, Incendiary, Cryo
Whereas Power-using classes use various powers to strip Protections, Soldiers use special ammunition to further improve the damage value per shot. This obviously relies on having ammunition. It does not modify Heavy Weapons.
With Ammo Powers, also switch weapons to deal with different types of protections, and thereby maximize damage versus any one type of protection.
Our recommended build ignores Cryo Ammo because it really only works on targets with no protection. Against such as target, there are various options to keep them neutralized -- the fire panic from Incendiary shots, weapons overheating from Disruptor shots, or a Concussive Shot to knock it down, and whatever we have from our choice of Advanced Training.
Shepard's squad is generally more useful in the background to provide Powers, so we recommend not taking the Squad version of ammunition powers.

Combat Mastery
Although Incinerate can be arced, it almost never hits a target in cover unless they stand up, which they can be made to do with Combat Drone.
Incinerate does half damage against synthetics, so once armor is down, Overload is better against synthetics.
Against targets without much shielding left, switch to Incinerate since Overload damages Health only against synthetics. For this reason, the Control Build does not try to maximize it.

Advanced Training: Reave
Reave is chosen for Advanced Training because it is good against Barriers, against which the Soldier does not have an Ammo type. It is also generically useful as an attack power, and has additional benefits against unprotected organic enemies:

The initial period of disability combined with the animation that lifts the target provides a period of fairly easy targeting, even without Adrenaline Rush.

Heals you and temporarily boosts health beyond the normal maximum.

If you take Reave, Concussive Shot is not important. Concussive Shot has the same cooldown except the cooldown time cannot benefit from Biotic Upgrades -- so you might as well use Reave as your backup out-of-ammunition attack.

Advanced Training: Slam
If you are not worried about running out of ammo stripping enemy protections, then Slam is a very good alternative to Reave. Like many powers, its effects really come into play only against unprotected targets. Slam has the advantage of having a very fast cooldown (3 second cooldown for Shepard) and the Crippling Slam rank 4 evolution will leave the target prone on the ground for 8 seconds and vulnerable to aimed shots, after which it is still helpless for a couple of seconds because it has to get up.